The set of all x values for which |f(x)

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Relations and Functions

Question:

The set of all x values for which |f(x) + g(x)| < |f(x)| + |g(x)| is true if f(x) = x – 3 and g(x) = 4 – x is given by

Options:

R -]3, 4[

R –[3, 4]

None of these

Correct Answer:

R –[3, 4]

Explanation:

$|f(x) + g(x)| < |f(x)| + |g(x)|$

$⇒|x-3+4-x| < |x-3|+|4-x|$

$1<|x-3|+|4-x|$

for equation if $x∈(3,4)$ then inequality doesn't hold

so R –[3, 4]